Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (12): 2367-2378    DOI: 10.3785/j.issn.1008-973X.2022.12.006
    
Decision method for product styling design based on single-valued neutrosophic sets and cloud clustering
Hui-ning PEI1(),Zhao-yun TAN1,Xin-yu LIU1,Bao-zhen TIAN2
1. School of Architecture and Art Design, Hebei University of Technology, Tianjin 300401, China
2. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030027, China
Download: HTML     PDF(1464KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

A multi-attribute decision method for product styling design based on single-valued neutrosophic sets (SVNS) and cloud model clustering was proposed, in order to obtain an objective and reasonable weight distribution. Decision-making experts were scientifically clustered, considering the limited rational psychological behavior characteristics and strategic manipulation behaviors. The square matrix of the pairwise comparison ratios of the standard attributes and the alternatives was constructed by the decision-making experts to obtain the SVNS. Mapping the three membership values of true, false, and uncertain in the single-valued neutrosophic cube (SVNC), the relative weight of the standard attributes was obtained by screening the evaluation results of the alternatives under each standard attribute. The cloud model clustering method fused with multi-granularity language was used to cluster decision-making experts, conflicting and unreasonable decision-making experts were eliminated to obtain effective design decision-making expert weights. The overall priority score of each alternative was calculated and sorted through the standard attribute weights and the weights of decision-making experts. The feasibility and effectiveness of the proposed method was verified by an example of car styling design scheme. Results show that using the proposed method, dishonest strategic manipulation is avoided and the multiple attribute decision making problem for car styling design in complex and uncertain situations is effectively solved.

Key words： product styling design      single-valued neutrosophic sets (SVNS)      cloud model clustering      multiple attribute decision making      multi-granularity language     
Received: 29 December 2021      Published: 03 January 2023
CLC:  C 934  
  TH 122  
Fund:  教育部人文社会科学基金资助项目（21YJCZH113）；河北省高等学校科学研究资助项目（SD201091）
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Hui-ning PEI
Zhao-yun TAN
Xin-yu LIU
Bao-zhen TIAN
Cite this article:

Hui-ning PEI,Zhao-yun TAN,Xin-yu LIU,Bao-zhen TIAN. Decision method for product styling design based on single-valued neutrosophic sets and cloud clustering. Journal of ZheJiang University (Engineering Science), 2022, 56(12): 2367-2378.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.12.006     OR     https://www.zjujournals.com/eng/Y2022/V56/I12/2367


基于单值中智集和云聚类的产品造型设计决策方法

为了获得客观、合理的权重分配，综合考虑有限理性心理行为特征和策略操控行为，把决策专家进行科学聚类，提出基于单值中智集（SVNS）和云模型聚类的产品造型设计多属性决策方法. 决策专家构造标准属性和备选方案的成对比较比率平方矩阵获得SVNS，映射真、假、不确定3个隶属度值到单值中智立方体（SVNC）中，筛选各标准属性下备选方案的评估结果，获得标准属性的相对权重. 利用融合多粒度语言的云模型聚类方法集群决策专家，淘汰存在冲突和非理性的决策专家，获得有效的设计决策专家权重. 由标准属性权重和决策专家权重，综合计算各备选方案的总体优先级得分并进行排序. 以汽车造型设计方案为例，验证所提方法的可行性和有效性. 结果表明，所提方法避免了恶意策略操作，有效地解决了复杂和不确定情况下的汽车造型设计多属性决策问题.


关键词： 产品造型设计,  单值中智集(SVNS),  云模型聚类,  多属性决策,  多粒度语言 
Fig.1 Multi-attribute decision-making framework for product styling design based on single-valued neutrosophic sets (SVNS)
Fig.2 Space division of single-valued neutrosophic sets (SVNC)
Fig.3 Framework for weight allocation of decision-making experts based on cloud model clustering
Fig.4 Design scheme of front view styling of car
Fig.5 Legend of evaluation criteria for car front view styling design scheme
A $x_i^{(j,m)} / x_l^{(j,m)}$
A1 A2 A3 A4 A5 A6
A1 1 1/5 3 1/2 1/3 4
A2 5 1 7 3 2 9
A3 1/3 1/7 1 1/3 1/5 1/2
A4 2 1/3 3 1 1/2 5
A5 3 1/2 5 2 1 6
A6 1/4 1/9 2 1/5 1/6 1
Tab.1 Pairwise comparison ratio square matrix of alternatives
${D_{\rm{M}}}$ $x_1^m, S_1^m$ $x_2^m, S_2^m$ $x_3^m, S_3^m$ $x_4^m, S_4^m$ $x_5^m, S_5^m$ $x_6^m, S_6^m$ $x_7^m, S_7^m$ $x_8^m, S_8^m$ ${\text{C} }{\text{.r} }.\left( {{\boldsymbol{R}}_{J \times J}^m} \right)$/%
$D_{\rm{M}}^1$ 0.028 3, 90 0.158 8, 85 0.041 8, 100 0.020 4, 80 0.330 6, 100 0.250 9, 95 0.070 4, 85 0.098 9, 90 3.46
$D_{\rm{M}}^2$ 0.067 7, 100 0.153 1, 85 0.030 7, 80 0.022 2, 95 0.345 9, 100 0.231 8, 90 0.045 6, 100 0.103 0, 85 2.49
$D_{\rm{M}}^3$ 0.066 7, 85 0.173 8, 75 0.029 9, 80 0.022 3, 70 0.358 8, 85 0.218 3, 70 0.043 4, 90 0.086 8, 75 5.61
$D_{\rm{M}}^4$ 0.067 1, 85 0.108 3, 90 0.019 7, 80 0.027 8, 90 0.349 2, 85 0.230 2, 75 0.047 1, 95 0.150 6, 95 4.10
$D_{\rm{M}}^6$ 0.063 8, 75 0.106 7, 80 0.018 9, 70 0.028 9, 85 0.359 5, 80 0.225 8, 70 0.048 7, 90 0.147 6, 90 5.20
$\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
$D_{\rm{M}}^{20}$ 0.068 5, 100 0.148 1, 80 0.030 6, 75 0.021 0, 95 0.367 1, 90 0.221 9, 85 0.044 5, 100 0.098 4, 90 3.15
Tab.2 Weights, concordance ratio and confidence scores of each decision-making expert for each standard
$B$ $x_1^{\left( {j, 1} \right)}, S_1^{\left( {j, 1} \right)}$ $x_2^{\left( {j, 1} \right)}, S_2^{\left( {j, 1} \right)}$ $x_3^{\left( {j, 1} \right)}, S_3^{\left( {j, 1} \right)}$ $x_4^{\left( {j, 1} \right)}, S_4^{\left( {j, 1} \right)}$ $x_5^{\left( {j, 1} \right)}, S_5^{\left( {j, 1} \right)}$ $x_6^{\left( {j, 1} \right)}, S_6^{\left( {j, 1} \right)}$ ${\text{C} }{\text{.r} }.\left( {{\boldsymbol{R}}_{J \times J}^1} \right)$/%
B1 0.102 5, 100 0.413 2, 95 0.050 6, 80 0.152 8, 85 0.247 9, 100 0.032 9, 90 1.99
B2 0.095 5, 85 0.410 6, 65 0.049 1, 45 0.150 5, 60 0.254 6, 75 0.039 6, 75 5.13
B3 0.087 8, 85 0.424 0, 80 0.051 7, 85 0.143 8, 95 0.255 4, 65 0.037 3, 100 3.28
B4 0.096 4, 80 0.411 9, 85 0.049 6, 75 0.145 1, 80 0.255 9, 70 0.041 1, 75 4.96
B5 0.100 8, 95 0.425 6, 100 0.039 1, 90 0.138 4, 85 0.253 7, 95 0.042 5, 70 3.46
B6 0.090 8, 60 0.432 0, 65 0.047 0, 85 0.136 2, 75 0.255 6, 50 0.038 5, 45 7.32
B7 0.096 1, 65 0.424 6, 70 0.049 4, 65 0.142 2, 60 0.255 5, 75 0.032 3, 80 2.76
B8 0.096 3, 85 0.418 4, 100 0.049 4, 80 0.151 5, 90 0.251 2, 60 0.033 2, 85 1.54
Tab.3 Concordance ratio and confidence score of decision-making expert $D_{\rm{M}}^1$ for each alternative under each standard
Fig.6 Single-valued neutrosophic sets spatial mapping
B ${\psi ^ * }_i^j$
A1 A2 A3 A4 A5 A6
B1 0.101 2 0.370 5 0.034 5 0.173 6 0.264 9 0.069 5
B2 0.100 3 0.367 3 0.034 9 0.175 5 0.264 7 0.069 9
B3 0.100 7 0.364 0 0.036 0 0.178 0 0.268 3 0.068 6
B4 0.111 0 0.357 5 0.035 0 0.166 4 0.268 6 0.064 5
B5 0.106 1 0.364 2 0.034 4 0.138 4 0.261 2 0.071 6
B6 0.103 4 0.355 7 0.033 9 0.175 1 0.274 9 0.071 9
B7 0.105 6 0.367 3 0.034 1 0.166 9 0.264 0 0.070 6
B8 0.105 7 0.365 4 0.035 3 0.171 3 0.263 2 0.069 4
$ x_i^G $ 0.104 3 0.363 2 0.034 5 0.161 4 0.265 9 0.070 7
Tab.4 Overall priority score of all alternatives under each standard
A hxy
$ {A_1} $ $ {A_2} $ $ {A_3} $
A1 0.5 0.4, 0.3, 0.5 0.5, 0.6, 0.7
A2 0.6, 0.7, 0.5 0.5 0.7, 0.8, 0.9
A3 0.5, 0.4, 0.3 0.3, 0.2, 0.1 0.5
A4 0.5, 0.6, 0.7 0.2, 0.3, 0.4 0.5, 0.8, 0.7
A5 0.6, 0.8, 0.5 0.3, 0.4, 0.5 0.7, 0.8, 0.9
A6 0.3, 0.2, 0.4 0.1, 0.3, 0.2 0.4, 0.2, 0.3
Tab.5 Partial raw data hesitant fuzzy reciprocal preference relations of decision-making expert $D_M^1 $
${D_{\rm{M}}}$ $O\left( {{\boldsymbol{R}}_1^{ {H_\gamma } } } \right)$ $O\left( {{\boldsymbol{R}}_2^{ {H_\gamma } } } \right)$ $O\left( {{\boldsymbol{R}}_3^{ {H_\gamma } } } \right)$ $ {\vartheta _\gamma } $ $D_{\rm{L}}^\gamma$ $r$
$D_{\rm{M}}^1$ 0 ?0.333 0 1 0.049 0.071
$D_{\rm{M}}^2$ 0 0 0 0 0.052 0.068
$D_{\rm{M}}^3$ 0 0 ?1 1 0.056 0.064
$D_{\rm{M}}^4$ 0 ?1.333 0 1 0.071 0.049
$\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
$D_{\rm{M}}^{20}$ 0 0 ?0.667 1 0.042 0.078
Tab.6 Opinion reliability deduced value of decision-making export
B $g_i^l $
A1 A2 A3 A4 A5 A6
$ {B_1} $ $ g_3^3 $ $ g_5^3 $ $ g_2^3 $ $ g_4^3 $ $ g_4^3 $ $ g_2^3 $
$ {B_2} $ $ g_6^3 $ $ g_7^3 $ $ g_6^3 $ $ g_7^3 $ $ g_7^3 $ $ g_5^3 $
$ {B_3} $ $ g_4^3 $ $ g_5^3 $ $ g_4^3 $ $ g_5^3 $ $ g_5^3 $ $ g_3^3 $
$ {B_4} $ $ g_2^3 $ $ g_4^3 $ $ g_1^3 $ $ g_3^3 $ $ g_3^3 $ $ g_0^3 $
$ {B_5} $ $ g_7^3 $ $ g_8^3 $ $ g_7^3 $ $ g_8^3 $ $ g_8^3 $ $ g_7^3 $
$ {B_6} $ $ g_7^3 $ $ g_8^3 $ $ g_6^3 $ $ g_7^3 $ $ g_8^3 $ $ g_6^3 $
$ {B_7} $ $ g_5^3 $ $ g_6^3 $ $ g_4^3 $ $ g_5^3 $ $ g_6^3 $ $ g_4^3 $
$ {B_8} $ $ g_5^3 $ $ g_7^3 $ $ g_5^3 $ $ g_6^3 $ $ g_6^3 $ $ g_4^3 $
Tab.7 Cloud model data for decision-making expert for each alternative under each standard
A ${\boldsymbol{R}}$ $t_{xy}^c $
$ {A_1} $ $ {A_2} $ $ {A_3} $ $ {A_4} $ $ {A_5} $ $ {A_6} $
$ {A_1} $ R1 0.128 0 0.162 7 0.097 2 0.139 2 0.170 1 0.093 2
R2 0 0.181 4 0.075 2 0.150 1 0.160 4 0.086 3
R3 0 0.164 2 0.092 5 0.151 5 0.171 3 0.096 1
$\vdots$
$ {A_6} $ R1 0.162 8 0.184 6 0.109 4 0.156 2 0.174 0 0.128 0
R2 0.169 6 0.187 0 0.116 1 0.148 7 0.156 4 0
R3 0.159 9 0.189 2 0.111 0 0.146 3 0.172 1 0
Tab.8 Group decision matrix under three fuzzy preference relations
Fig.7 Comparison chart of overall score results of different decision methods
决策方法 e/% t/min
4个备选方案 6个备选方案 4个备选方案 6个备选方案
本研究 4.82 6.91 1.37 1.91
SVNS 5.07 9.30 1.19 1.75
VIKOR 11.13 18.62 0.53 0.84
BWM 12.29 20.46 0.78 0.95
Tab.9 Comparison of decision performance results
[1]   赵萌, 秦金磊, 潘一如, 等 基于策略权重的模糊多属性决策方法[J]. 控制与决策, 2021, 36 (5): 1259- 1267
ZHAO Meng, QIN Jin-lei, PAN Yi-ru, et al Strategic weight manipulation in fuzzy multiple attribute decision making[J]. Control and Decision, 2021, 36 (5): 1259- 1267
doi: 10.13195/j.kzyjc.2019.0542
[2]   OCAMPO L A, LABRADOR J J T, JUMAO-AS A M B, et al Integrated multiphase sustainable product design with a hybrid quality function deployment-multi-attribute decision-making (QFD-MADM) framework[J]. Sustainable Production and Consumption, 2020, 24: 62- 78
doi: 10.1016/j.spc.2020.06.013
[3]   陈六新, 罗南方 基于前景理论的勾股模糊多属性决策[J]. 系统工程理论与实践, 2020, 40 (3): 726- 735
CHEN Liu-xin, LUO Nan-fang Pythagorean fuzzy multi-criteria decision-making based on prospect theory[J]. Systems Engineering-Theory and Practice, 2020, 40 (3): 726- 735
doi: 10.12011/1000-6788-2018-2422-10
[4]   杨涛, 杨育, 薛承梦, 等 考虑客户需求偏好的产品创新设计方案多属性决策评价[J]. 计算机集成制造系统, 2015, 21 (2): 417- 426
YANG Tao, YANG Yu, XUE Cheng-meng, et al Multi-attribute decision-making evaluation method for product innovation design scheme with demand preferences of customers[J]. Computer Integrated Manufacturing Systems, 2015, 21 (2): 417- 426
doi: 10.13196/j.cims.2015.02.014
[5]   CHEN Z, YANG L, RODRÍGUEZ R M, et al Power-average-operator-based hybrid multiattribute online product recommendation model for consumer decision-making[J]. International Journal of Intelligent Systems, 2021, 36 (6): 2572- 2617
doi: 10.1002/int.22394
[6]   MAO L X, LIU R, MOU X, et al New approach for quality function deployment using linguistic Z-numbers and EDAS method[J]. Informatica, 2021, 32 (3): 565- 582
[7]   MOHANTY P P, MAHAPATRA S S, MOHANTY A, et al A novel multi-attribute decision making approach for selection of appropriate product conforming ergonomic considerations[J]. Operations Research Perspectives, 2018, 5: 82- 93
doi: 10.1016/j.orp.2018.01.004
[8]   JAIN R, RANA K B, MEENA M L. An integrated multi-criteria decision-making approach for identifying the risk level of musculoskeletal disorders among handheld device users [J/OL]. Soft Computing, 2021: 1-11[2021-02-03]. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7856850/pdf/500_2021_Article_5592.pdf.
[9]   ARIFIN Z, PRASETYO S D, PRABOWO A R, et al Preliminary design for assembling and manufacturing sports equipment: a study case on aerobic walker[J]. International Journal of Mechanical Engineering and Robotics Research, 2021, 10 (3): 107- 115
[10]   ZADEH L A Fuzzy sets[J]. Information and Control, 1965, 8 (3): 338- 353
doi: 10.1016/S0019-9958(65)90241-X
[11]   ATANASSOV K T Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20 (1): 87- 96
doi: 10.1016/S0165-0114(86)80034-3
[12]   TORRA V Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25 (1): 529- 539
[13]   SMARANDACHE F. A unifying field in logics [M]. [S.l.]: American Research Press, 2003.
[14]   WANG H, SMARANDACHE F, ZHANG Y, et al Q-single valued neutrosophic soft sets[J]. Journal of New Theory, 2016, (13): 10- 25
[15]   LI J, FANG H, SONG W Sustainable supplier selection based on SSCM practices: a rough cloud TOPSIS approach[J]. Journal of Cleaner Production, 2019, 222: 606- 621
doi: 10.1016/j.jclepro.2019.03.070
[16]   WANG P, HUANG S, CAI C Dual linguistic term set and its application based on the normal cloud model[J]. IEEE Transactions on Fuzzy Systems, 2021, 29 (8): 2180- 2194
doi: 10.1109/TFUZZ.2020.2994994
[17]   MA Z, ZHANG S Risk-based multi-attribute decision-making for normal cloud model considering pre-evaluation information[J]. IEEE Access, 2020, 8: 153891- 153904
doi: 10.1109/ACCESS.2020.3018153
[18]   WANG P, XU X, HUANG S, et al A linguistic large group decision making method based on the cloud model[J]. IEEE Transactions on Fuzzy Systems, 2018, 26 (6): 3314- 3326
doi: 10.1109/TFUZZ.2018.2822242
[19]   GRZYBOWSKI A Z Note on a new optimization based approach for estimating priority weights and related consistency index[J]. Expert Systems with Applications, 2012, 39 (14): 11699- 11708
doi: 10.1016/j.eswa.2012.04.051
[20]   SAATY T L, VARGAS L G. Decision making with the analytic network process [M]. [S.l.]: Springer, 2006.
[21]   XU Y, XI Y, CABRERIZO F J, et al An alternative consensus model of additive preference relations for group decision making based on the ordinal consistency[J]. International Journal of Fuzzy Systems, 2019, 21 (6): 1818- 1830
doi: 10.1007/s40815-019-00696-w
[22]   PENG H G, ZHANG H Y, WANG J Q, et al An uncertain Z-number multicriteria group decision-making method with cloud models[J]. Information Sciences, 2019, 501: 136- 154
doi: 10.1016/j.ins.2019.05.090
[23]   WANG H, FANG Z G, WANG D A, et al An integrated fuzzy QFD and grey decision-making approach for supply chain collaborative quality design of large complex products[J]. Computers and Industrial Engineering, 2020, 140: 106212
doi: 10.1016/j.cie.2019.106212
[24]   LI S, MA X, YANG C A combined thermal power plant investment decision-making model based on intelligent fuzzy grey model and ito stochastic process and its application[J]. Energy, 2018, 159: 1102- 1117
doi: 10.1016/j.energy.2018.06.184
[25]   TSENG M L, WU K J, HU J Y, et al Decision-making model for sustainable supply chain finance under uncertainties[J]. International Journal of Production Economics, 2018, 205: 30- 36
doi: 10.1016/j.ijpe.2018.08.024
No related articles found!